RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers

RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1

Question 1.
Simplify the following:

Solution:

Question 2.
If a = 3 and b =-2, find the values of:
(i) a ^a + b ^b
(ii) a ^b + b ^a
(iii) (a+b) ^ab
Solution:

Question 3.
Prove that:

Solution:

Question 4.
Prove that

Solution:

Question 5.
Prove that

Solution:

Question 6.

Solution:

Question 7.
Simplify the following:

Solution:

Question 8.
Solve the following equations for x:

Solution:

Question 9.
Solve the following equations for x:

Solution:

Question 10.
If 49392 = a ⁴ b ² V ³ , find the values.of a, b and c, where a, b and c are different positive primes.
Solution:

Question 11.
If 1176 = 2 ^a x 3 ^b x T ^c , find a, 6 and c.
Solution:

Question 12.
Given 4725 = 3 ^a 5 ^b 7 ^c , find:
(i) the integral values of a, b and c
(ii) the value of 2 ^-a 3 ^b 7 ^c
Solution:

Question 13.
If a = xy ^p-1 , b = xy ^{q -1} and c = xy ^r-1 , prove that a ^q-r b ^r-p c ^p-q = 1
Solution:

RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers E x 2.2

Question 1.
Assuming that x, y, z are positive real numbers, simplify each of the following:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Prove that:

Solution:

Question 4.
Show that:


Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Find the values of x in each  of the following:

Solution:

Question 11.
If x = 2 ^{1 /3} + 2 ^2/3 , show that x ³ – 6x = 6.
Solution:

Question 12.
Determine (8x) ^x , if 9 ^{x + 2} = 240 + 9 ^x .
Solution:

Question 13.
If 3 ^{x + 1} = 9 ^{x- 2} , find the value of 2 ^{1 +x} .
Solution:

Question 14.
If 3 ^4x = (81) ^-1 and 10 ^1/y = 0.0001, find the value of 2 ^-x+4y
Solution:

Question 15.
If 5 ^3x = 125 and 10 ^y = 0.001 find x and y.
Solution:

Question 16.
Solve the following equations:


Solution:

Question 17.

Solution:

Question 18.
If a and b are different positive primes such that

Solution:

Question 19.
If 2 ^x x 3 ^y x 5 ^z = 2160, find x, y and z. Hence, compute the value of 3 ^x x 2 ^-y x 5 ^-z .
Solution:

Question 20.
If 1176 = 2 ^a x 3 ^b x 7 ^c , find the values of a, b and c. Hence, compute the value of 2 ^a x 3 ^b x 7 ^-c as a fraction.
Solution:

Question 21.
Simplify:

Solution:

Question 22.
Show that:

Solution:

Question 23.

Solution:

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers VSAQS

Question 1.
Write (625) ^{– 1/4} in decimal form.
Solution:

Question 2.
State the product law of exponents:
Solution:
x ^m x x ⁿ = x ^{m +n}

Question 3.
State the quotient law of exponents.
Solution:
x ^m ÷ x ⁿ = x ^{m -n}

Question 4.
State the power law of exponents.
Solution:
(x ^m ) ⁿ =x ^{m x n} = x ^mn

Question 5.
If 2 ⁴ x 4 ² – 16 ^x , then find the value of x.
Solution:

Question 6.

Solution:

Question 7.
Write the value of \(\sqrt [ 3 ]{ 7 }\)  x \(\sqrt [ 3 ]{ 49 }\) .
Solution:

Question 8.

Solution:

Question 9.
Write the value of \(\sqrt [ 3 ]{ 125×27 }\)
Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.
If (x – 1) ³ = 8, what is the value of (x + 1) ² ?
Solution:

Class 9 RD Sharma Solutions Chapter 2 Exponents of Real Numbers MCQS

Mark the correct alternative in each of the following:
Question 1.
The value of {2 – 3 (2 – 3) ³ } ³ is
(a) 5
(b) 125
(c) \(\frac { 1 }{ 5 }\)
(d) -125
Solution:
{2 – 3 (2 – 3) ³ } ³ = {2 – 3 (-1) ³ } ³
= {2 – 3 x (-1)} ³
= (2 + 3) ³ = (5) ³
= 125    (b)

Question 2.
The value of x – y ^x-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
Solution:
x = 2, y = -2
x-y ^x-y = 2 – (-2) ^{2 – (-2)}
= 2 – (-2) ^{2 + 2} = 2 – (-2) ⁴
= 2 – (+16) = 2 – 16 = -14        (d)

Question 3.
The product of the square root of x with the cube root of x, is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Solution:

Question 4.
The seventh root of x divided by the eighth root of x is

Solution:

Question 5.
The square root of 64 divided by the cube root of 64 is
(a) 64
(b) 2
(c) \(\frac { 1 }{ 2 }\)
(d) 64 ^{\(\frac { 2 }{ 3 }\)}
Solution:

Question 6.
Which of the following is (are) not equal to

Solution:

Question 7.
When simplified (x ^{– 1} + y ^{– 1} ) ^{– 1} is equal to

Solution:

Question 8.
If 8 ^{x +1} = 64, what is the value of 3 ^{2x +1} ?
(a) 1
(b) 3
(c) 9
(d) 27
Solution:

Question 9.
If (2 ³ ) ² = 4 ^x then   3 ^x =
(a) 3
(b) 6
(c) 9
(d) 27
Solution:

Question 10.
If x ^-2 = 64, then x ^{\(\frac { 1 }{ 3 }\)} + x°=
(a) 2
(b) 3
(c) \(\frac { 3 }{ 2 }\)
(c) \(\frac { 2 }{ 3 }\)
Solution:

Question 11.
When simplified ( –\(\frac { 1 }{ 27 }\)) ^{\(\frac { -2 }{ 3 }\)}
(a) 9
(b) -9
(c) \(\frac { 1 }{ 9 }\)
(d) –\(\frac { 1 }{ 9 }\)
Solution:

Question 12.
Which one of the following is not equal to

Solution:

Question 13.
Which one of the following is not equal to

Solution:

Question 14.
If a, b, c are positive real numbers, then

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.


Solution:

Question 21.
The value of {(23 + 2 ² ) ^2/3 + (150 -29) ^1/2 } ² is
(a) 196
(b) 289
(c) 324
(d) 400
Solution:
{(23 + 2 ² ) ^{2 / 3} + (150 – 29) ^1/2 } ²
= [(23×4) ^{\(\frac { 2 }{ 3 }\)} +(150 – 29) ^{\(\frac { 1 }{ 2 }\)} ] ²
= [(27) ^{\(\frac { 2 }{ 3 }\)} + (121) ^{\(\frac { 1 }{ 2 }\)} ] ²
= [(3 ³ ) ³ +(11 ² ) ^{\(\frac { 1 }{ 2 }\)} ] ² = (9 + 11) ²
= (20) ² = 400  (d)

Question 22.
(256) ^0.16 x (256) ^0.09
(a) 4
(b) 16
(c) 64
(d) 256.25
Solution:

Question 23.
If 10 ^2y = 25, then 10 ^-y equals

Solution:

Question 24.
If 9 ^{X + 2} = 240 + 9 ^X . then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1
Solution:

Question 25.
If x is a positive real number and x ² = 2, then x ³ =
(a) \(\sqrt { 2 } \)
(b) 2\(\sqrt { 2 } \)
(c) 3\(\sqrt { 2 } \)
(d) 4
Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.

Solution:

Question 29.

Solution:

Question 30.

Solution:

Question 31.

Solution:

Question 32.

Solution:

Question 33.
If (16) ^{2x + 3} = (64) ^{x + 3} , then 4 ^{2x – 2} =
(a) 64
(b) 256
(c) 32
(d) 512
Solution:

Question 34.


Solution:

Question 35.


Solution:

Question 36.

Solution:

Question 37.

Solution:

Question 38.

Solution:

Question 39.

Solution:

Question 40.

Solution:

RD Sharma Class 9th Solutions Chapter 2 Exponents of Real Numbers Exercise 2.1

Q1 Q2 Q3 Q4 Q5

RD Sharma Class 9 Solutions